Questions tagged [numerical-methods]

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Solving option market making problem

I am currently working on a paper for quoting option as a market maker from Bastien Baldacci , Philippe Bergault & Olivier Guéant Without dwelling on details on how to obtain the HJB equation for ...
Kupoc's user avatar
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7 votes
2 answers
299 views

Likelihood ratio and pathwise sensitivity method for coupled SDEs

I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\ \end{align*} where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
user107224's user avatar
6 votes
0 answers
206 views

SABR-LMM: best way to perform a MC simulation

I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$: $$ \begin{align} &\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
BEQuant's user avatar
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6 votes
1 answer
412 views

Importance sampling for Monte Carlo with local volatility in practice

I am given a diffusion with a local volatility to price barrier options: $$dX(t)=X(t)\mu dt+X(t)\sigma(t,X)dW_t$$ I want to use Importance Sampling to price barrier options "far" out of the ...
user56787's user avatar
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6 votes
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255 views

Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
TheBridge's user avatar
  • 4,563
5 votes
0 answers
145 views

Integrated Delta does not seem to be smooth (ATM, Heston)

I am interested in an integrated call option that removes the dependence on time, $$I(S)=\int_0^\infty C(S,t)\text{d}t.$$ Because the value of a call option is a smooth function, I expect this ...
Kevin's user avatar
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5 votes
0 answers
174 views

Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
Dimitri Vulis's user avatar
4 votes
2 answers
574 views

Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
Sanjay's user avatar
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3 votes
0 answers
401 views

Implementation of solvers for curve construction

I'd be really interested to hear people's experiences of implementing global solvers for curve construction, especially with regard to how robust the approach is in practice, numerical performance, ...
Marco's user avatar
  • 139
3 votes
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Verify mean-square convergence of the Euler-maruyama scheme numerically

I have a question about the order of convergence of the Euler-Maruyama scheme and how one verifes this numerically. I have read that the Euler-Maruyama scheme is mean-squared convergent of order 1/2 ...
user202542's user avatar
3 votes
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613 views

Is there a more efficient data structure to implement binomial trees than 2d array?

I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes. ...
Vim's user avatar
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3 votes
0 answers
94 views

Time discretisations, FDM vs FEM

I am interested in adaptive mesh methods for numerical solution of PDEs with applications to finance. As part of a school project, I have been pricing vanilla European call and put options using 2D ...
turtlesandwich's user avatar
3 votes
0 answers
480 views

What R-packages for SOCP problems are there?

Currently, I am looking deeper into the topic of second-order cone programming. Could you suggest packages that solve SOCP-problems in R? With your answer, please provide a short description of ...
vanguard2k's user avatar
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2 votes
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87 views

Measure of the behavior of Swaption surface

I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope. Let ...
Michael W's user avatar
2 votes
0 answers
98 views

Antoine Savine's store

In his book "Modern Computational Finance, AAD and Parallel Simulation", Antoine Savine writes page 263 in the footnote : "We could have more properly implemented the store with GOF’s ...
11house's user avatar
  • 113
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106 views

State-of-the-art grid construction techniques

I am wondering what the state-of-the-art regarding grid definition and construction, for solving PDEs using finite differences. I know some techniques are described in Duffy's Finite difference ...
KT8's user avatar
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120 views

Numerical scheme for this HJB equation

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...
Kupoc's user avatar
  • 98
2 votes
0 answers
161 views

Bermudan pricing in Black-Scholes

Is there an "analytical" method to price American options (approximated as daily Bermudans) in the Black-Scholes model using backward induction? $$V_T(S) = \max(K-S, 0)$$ $$V_{T-\Delta t}(S) ...
user357269's user avatar
2 votes
0 answers
285 views

Solve the Schwartz mean reverting PDE for option pricing using Euler explicit method (matlab)

Objective: Implement the Euler Explict Method for solving the PDE for option prices under the Schwartz mean reverting model. The price evolution of a commodity can be described by the Schwartz SDE $$...
sound wave's user avatar
2 votes
0 answers
50 views

Transforming and minimisation of the BS PDE

I'm trying a novel numerical substitution/fitting method to solve the BS PDE, but the issue is that due to the large range of magnitude of prices $V(s,t)\in[10^{-20},10^1]$, when I try to minimise the ...
Sam Palmer's user avatar
2 votes
0 answers
175 views

Practical precision for Options Pricing

When pricing options, especially in the theoretical literature getting high precision, say up to 8 decimal places is always a competitive goal. Though realistically in a practical setting is such ...
Sam Palmer's user avatar
2 votes
0 answers
356 views

Portfolio optimization with absolute position constraints

I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions. I've been experimenting with QP, ...
user5980's user avatar
  • 131
2 votes
0 answers
187 views

Practical quantitative finance problems that could be solved in trustless grid computing environment?

Are there any relevant computationally intensive quantitative finance problems that could be outsourced to a trustless grid? By a trustless grid I mean that you cannot trust it with the access to your ...
Alexey Kalmykov's user avatar
1 vote
1 answer
230 views

Issues with calculating IV with options bar data

I am currently working with some options OHLC data (30 minute bars) from IBKR for a range of strike prices, maturities and for both calls/puts. For each bar, I am trying to back out the IV (crudely ...
des224's user avatar
  • 93
1 vote
0 answers
92 views

Choice of grid for numerical integration

I have to compute an integral involving the characteristic function for pricing options in a model and it so happens that accurate approximation seems to be mostly about putting lots of points in ...
Stéphane's user avatar
  • 2,456
1 vote
0 answers
186 views

Programming the Milstein method and computing the increments

In the wikipedia article on the Milstein method, the following python code to simulate a geometric Brownian motion is presented: ...
StefanH's user avatar
  • 201
1 vote
0 answers
163 views

Implicit Scheme for Cox-Ingersoll-Ross Model PDE

I am considering the PDE for the price of a bond $V(r,t)$ with maturity $T$ under the Cox-Ingersoll-Ross model, $$V_t+\frac12\sigma^2rV_{rr}+\nu(\theta-r)V_r-rV=0\quad r>0, t\in(0,1)$$ with ...
user107224's user avatar
1 vote
0 answers
47 views

Quick Discretization question for finite difference and finite element methods

Assume we have the discretization in space $x_1, x_2, ... , x_M$ and time $t_1, t_2, ... , t_N$ for a finite difference or finite element method for option pricing and we want to solve for the option ...
sigma1988's user avatar
1 vote
0 answers
79 views

boundary conditions in finite element method

In the appendix A of this paper, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.227.5073&rep=rep1&type=pdf, a finite element method is demonstrated to price a straddle. The same ...
sigma1988's user avatar
1 vote
0 answers
675 views

CIR model. Is there a closed-form solution or even a good proxy of analytical solution?

Is there a closed-form (analytical) solution for the Cox-Ingersoll-Ross SDE \begin{equation} dr_t=k_r(\theta_r-r_t)dt+\sigma_r\sqrt{r_t}dW_t\tag{1} \end{equation} ? Notice that $\{r_t\}$ is our ...
Strictly_increasing's user avatar
1 vote
0 answers
91 views

Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ...
Gert van Dasler's user avatar
1 vote
0 answers
181 views

Longstaff Schwartz method (LSM): how to increase accuracy?

In the LSM method, I am currently (as they do in the paper) using weighted Laguerre polynomials as basis functions, about 3-5 of them. If I wish to increase the accuracy of my model, what should I do?...
early's user avatar
  • 11
1 vote
0 answers
145 views

How is it possible that the measurement uncertainty in Kalman Filter is less than 0?

In Euan Sinclair's Option Trading, Pricing and Volatility Strategies and Techniques, it mentions that the true value of the price can be estimated via Kalman Filter: $$S_\mathrm{new} = S + k (S_b − S)...
Doe's user avatar
  • 11
1 vote
0 answers
127 views

Numerical Solutions to PDEs with Financial Applications

I am reading a paper by Richard White, Opengamma named Numerical Solutions to PDEs with Financial Applications. There is an implementation codes as stated in paper hosted at https://opengamma.com/...
TryingtobeQuant's user avatar
1 vote
0 answers
87 views

How good is a "good accuracy" in pricing?

Say you want to test various numerical algorithms for purposes of pricing. How close do you need to be to some benchmark value (the "actual" price) for your accuracy to be good? Say I am trying to ...
Methods's user avatar
  • 11
1 vote
0 answers
176 views

What is the best source to get 10 milliseconds time-series data for numerical computation?

I am working with 4th order Runge-Kutta method to compute a second order differential equation. For the best accuracy, I need a 10 milliseconds ohlcv time-series data. I know that I can build it ...
Bouarfa Mahi's user avatar
1 vote
0 answers
136 views

Optimal allocation problem by finite differences

I am attempting to apply implicit finite difference to solve Merton's problem of optimal portfolio allocation for constant parameters. The equation to solve is the Hamilton-Jacobi-Bellman equation: $$...
scrps93's user avatar
  • 113
1 vote
0 answers
296 views

Adjoint Algorithmic Differentiation: swap pricing

I have tried to implement an AAD routine to price call options using the Black-Scholes formula, but my greeks are not quite agreeing with the expected ones, so I have decided to start with something a ...
Alfie's user avatar
  • 223
1 vote
0 answers
226 views

School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
Sanjay's user avatar
  • 1,637
1 vote
0 answers
71 views

Jacobian for Newton method for American options by front fixing

In this paper Penalty and front-fixing methods for the numerical solution of American option problems a front fixing method based on Newton is described for an American put option is described. I am ...
Moneyness's user avatar
1 vote
0 answers
35 views

Stiffness of numerical methods for SDE

What can I do with stiffness of numerical methods for SDE? I want to use numerical approach for solving SDE in market's scenarios generation. Is there any general approach to handle it?
Vlad Pimkin's user avatar
1 vote
0 answers
136 views

Order 1.5 strong SDE integration methods for systems with diagonal additive noise

I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ...
horchler's user avatar
  • 123
1 vote
1 answer
8k views

estimate implied volatility using newton-raphson in python

I am trying to calculate the implied volatility using newton-raphson in python, but the value diverges instead of converge. What is wrong with the code? ...
user2686641's user avatar
0 votes
1 answer
245 views

Choosing a time step in Monte Carlo simulation of forward rates in LIBOR Market Model

Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps ...
Hasek's user avatar
  • 794
0 votes
0 answers
53 views

Computation of an integral containing d ln x (Scale of Market Shocks)

I am trying to implement a Scale of Market Shocks method (SMS) which was presented in a 1999 working document by Olsen & Associates named Introducing a Scale of Market Shocks and later refined in ...
dqd's user avatar
  • 101
0 votes
0 answers
37 views

Transform the payoff to be non-zero

Is there any way to transform the basic call option payoff $V(s,0) = \max(s-K,0)$ such that $g(V(s,0))\neq 0$ $\forall s $, where $g()$ is the transform function of the payoff. This is to use in a ...
Sam Palmer's user avatar
0 votes
0 answers
67 views

what is the meaning of $U^{n+1/3}$ ADI method

For the ADI in numerical method $$\frac{U^{n+1/3}-U^n}{k/3} = \Delta^2_x U^{n+1/3} + \Delta^2_y U^n + \Delta^2_z U^{n+2/3}$$ $$....$$ $$....$$ don't like $U^{n+1/2} = \dfrac 1 2 (U^{n+1}+U^n),$ I ...
A.Oreo's user avatar
  • 1,243
-1 votes
1 answer
97 views

Improving control variate for variance reduction

I have tried stock price as control variate for my monte carlo simulation, and I am trying to reduce the variance of my estimated price for European Put option. And the code look like this: ...
Lin Lex's user avatar
  • 17
-1 votes
2 answers
705 views

Numerical computation of Heston model Integral: Simpsone Rule or Gauss-Legendre Method

I want to price a call option using the Heston model for a given set of parameters. theory from URL: http://elis.sigmath.es.osaka-u.ac.jp/research/Heston-original.pdf The integral equation (18) ...
Matthias's user avatar